Answer :
Sure! Let's break down how to choose the correct standard form for the number [tex]\(2.31002 \times 10^{-4}\)[/tex].
### Understanding Standard Form:
Standard form for a number in scientific notation [tex]\(a \times 10^n\)[/tex], where:
- [tex]\(a\)[/tex] is a number greater than or equal to 1 and less than 10.
- [tex]\(n\)[/tex] is an integer that shows the power of 10 by which the number [tex]\(a\)[/tex] should be multiplied.
In this case, [tex]\(a = 2.31002\)[/tex] and [tex]\(n = -4\)[/tex].
### Step-by-Step Solution:
1. Interpreting the Power of 10:
The exponent [tex]\(-4\)[/tex] indicates that we need to move the decimal point 4 places to the left.
2. Moving the Decimal Point:
Start with [tex]\(2.31002\)[/tex]. Moving the decimal point 4 places to the left:
[tex]\[
2.31002 \rightarrow 0.231002 \rightarrow 0.0231002 \rightarrow 0.00231002 \rightarrow 0.000231002
\][/tex]
3. Comparing with Given Options:
Now, let's compare this number with the given choices:
- 0.00231002
- 0.0000231002
- 0.000231002
- [tex]\(-23,100.2\)[/tex]
e. Among these options, 0.000231002 is the correct representation of [tex]\(2.31002 \times 10^{-4}\)[/tex].
So, the correct standard form is:
[tex]\[
\boxed{0.000231002}
\][/tex]
It's important to understand how we move the decimal point according to the power of 10 in scientific notation. Each negative exponent means moving the decimal point to the left.
I hope this makes it clear! If you have any other questions, feel free to ask!
### Understanding Standard Form:
Standard form for a number in scientific notation [tex]\(a \times 10^n\)[/tex], where:
- [tex]\(a\)[/tex] is a number greater than or equal to 1 and less than 10.
- [tex]\(n\)[/tex] is an integer that shows the power of 10 by which the number [tex]\(a\)[/tex] should be multiplied.
In this case, [tex]\(a = 2.31002\)[/tex] and [tex]\(n = -4\)[/tex].
### Step-by-Step Solution:
1. Interpreting the Power of 10:
The exponent [tex]\(-4\)[/tex] indicates that we need to move the decimal point 4 places to the left.
2. Moving the Decimal Point:
Start with [tex]\(2.31002\)[/tex]. Moving the decimal point 4 places to the left:
[tex]\[
2.31002 \rightarrow 0.231002 \rightarrow 0.0231002 \rightarrow 0.00231002 \rightarrow 0.000231002
\][/tex]
3. Comparing with Given Options:
Now, let's compare this number with the given choices:
- 0.00231002
- 0.0000231002
- 0.000231002
- [tex]\(-23,100.2\)[/tex]
e. Among these options, 0.000231002 is the correct representation of [tex]\(2.31002 \times 10^{-4}\)[/tex].
So, the correct standard form is:
[tex]\[
\boxed{0.000231002}
\][/tex]
It's important to understand how we move the decimal point according to the power of 10 in scientific notation. Each negative exponent means moving the decimal point to the left.
I hope this makes it clear! If you have any other questions, feel free to ask!